The Universal Law of Gravitation
We saw that the gravitational force is the attractive force between any two objects with non-zero mass & seperated by a distance.
So does the Apple fall towards the Earth or does the Earth move towards the Apple?
Or do both move towards each other?. It’s actually simple logic! This is the Earth, and say this minuscule object is an Apple.
Based on what we learnt about the gravitational force, both apply an equal force to attract the other object towards itself. So if the forces are equal which one will accelerate more?
Based on the Newton’s second law, we know that the force applied is the product of mass and acceleration.
So the acceleration will equal ‘Force over the mass’. The acceleration is inversely proportional to the mass. If the mass is more, the acceleration will be lesser.
As the mass of the Earth is MUCH MUCH MUCH more than the mass of the Apple, It is the Apple that accelerates towards the Earth and not the other way around. Hope that makes it clear.
Now the question is ‘how do we quantify this force?’
To understand this, we need to understand a simple concept! And this simple concept is called the Universal law of Gravitation.
Say there are two objects A and B separated by a distance ‘d’.
The distance between the centres is considered the distance between the 2 objects and not this distance.
Assume that the mass of object A is ‘m1’ and that of object B is ‘m2’.
As object A is bigger, let’s assume ‘m1’ to be bigger than ‘m2’.
The Universal law of gravitation says that, ‘Every object in the universe attracts every object with a force which is DIRECTLY proportional to the product of their masses and INVERSELY proportional to the SQUARE of the distance between them’.
Let me repeat.
The force is Directly proportional to the PRODUCT of their masses and INVERSELY proportional to the SQUARE of the distance between them.
With this data, we can write it mathematically like this.
So if the mass of any of the objects increases, the gravitational force will have more magnitude. And more the distance between the two objects, the lesser will the gravitational force! Directly proportional to the product of the masses, and inversely proportional to the square of the distance between them.
This can be written as F equals G times m1 one times m2 over ‘d’ squared. ‘G’ here is the Constant of proportionality and is called the UNIVERSAL GRAVITAITONAL CONSTANT.
The equation can be modified and written as G equals ‘F times d squared’ over ‘m1 times m2’. The value of ‘G’ was found out by Lord Henry Cavendish using a Torsion Balance.
The universally accepted value of G is ‘six point six seven three’ times ‘ten raised to negative 11’.
What will be the units of G? Force is Newtons.
As the distance is in meters, we have ‘meters squared’. And as the mass is measured using kilograms, we multiply this with ‘kilograms raised to negative 2’. This is the value of the Universal gravitational constant!
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